The Geophysical Fluid Dynamics Institute
Florida State University
TPllahassee, Florida

The information contained in this paper was developed Liji-r the
auspices of the Florida Sea Grant College Program, with support from
the liOAA'Office of Sea Grant, U. S. Department of Commerce, :grant
number n4-6-158-44 This document- is a Technical Paper of the'State
University System .of Florida Sea Grant College Program, 2001 McCarty
Hall, University of Florida, Gainesville, FL 32611. Technical Papers"
are duplicated in limited quantities for specialized audiences requiring
rapid-access to information, which may be unedited.

Deceriber 1976

PREFACE

This report consists of two parts. Part I contains

5 technical papersk.by Barcilon, Lau, Miller, Tam and Travis,

all of which are published in scientific journals with high

standards of review. The first four of these cover results

of our early work under the-Sea Grant program. These papers

provide insight into the mechanisms of formation of transverse

sand bars, submarine longshore bars and rip currents. The

fifth paper is a thorough review paper in which theoretical and

experimental modelling of physical processes pertaining to the

near shore are discussed and compared with field observations.

Part II, by.Christopher Miller, presents the final computer model

for predicting changes in the plan shape of shorelines due to

the littoral drift component. This part of the report includes

a discussion of how the sediment transport rate is related empiri-

cally to the water flow; the range of incident wave angles for

which the governing equations are stable, the finite difference

scheme, as well as a listing of the computer program. It also

includes a test of the model on specific coastal sites in Florida.

PART I: The study of longshore bars has led to the con-

viction that the dredging of certain submarine longshore :bar

systems may actually lead to severe erosion of the shoreline.

A further suggco-ion has, been made concerning the possibility

of reversing erosion trends in some beach locations by properly

*Editorialnote: The five papers are included by reference only, ds they
appear in the literature already.

The paper by Lau and Barcilon (1972) investigates the
reflection and non-linear interaction between the first and
second harmonics of a two-dimensional BousSinesq wave train.
Effects of topography are included, with the depth departing
from a constant in a finite region. It is'found that topogra-
phy can speed up or reward energy transfer between the first
and second harmonics. The reflection coefficient is signifi-
cantly different from the one obtained by using linear theory.

In the paper by Barcilon and Lau (1973).an extension
of Kennedy's potential model is used to investigate the forma-
tion of sand bars normal to a gently sloping beach. The results
show that the spacing between the transverse bars depends upon
the inverse of the beach slope and upon th& square of the drift
velocities across the bars.- In spite of certain drawbacks the
theoretical predictions compare well with several observational
studies.

The paper by Lau and Travis (1973) investigates the mass
transport velocity in the Stokes boundary layer due to slowly
var :. Sto 'av.-s 1ipingrl ingr on and reflecting from a plane-

tion is interpreted to indicate the possible locations of sub-
marine longshore sand-bar formation. It is found that the num-
ber of bars is likely to increase when the;bottom gradient is
slight and that the spacing between the crests of the bars in-
creases seaward. for some distance offshore. These results are in
qualitative agreement with field observations.

The.paper by Tam (1973) investigates the dynamics of -
rip currents using shallow water equations with a horizontal
eddy viscosity term. In this paper similarity solutions of the
model equations are found which appear to..give reasonable repre-
sentations of the velocity profile and other characteristics of
rip currents.

a. Set value of constants appearing in expression for
longshore current
b. Compute coefficient, T, the ratio between the sand
and water transport rates

3. Subroutine ADJUST

a. Read in values of breaker height, angle, .and dura-
tion (fractional) of a particular wave type for
each beach segment; compute transport rates
b. We expect the angle of wave attack to change as
the beach orientation is altered. An adjustmentt"
angle, the difference between the old and new beach
angles, is added to the original (b and a revised
transport figure is calculated. This is done at
time intervals chosen by the user. Any accompany-
ing refractive modification of wave height is
considered secondary and is -neglected.

4. Subroutine INITL

Generate all necessary starting values for use by the
Hamming :scheme as outlined.in section V.

5. Subroutine DERIV

a. Given the beach coordinates compute the beach seg-
ment angles and the spacing between adjacent points.
b. Given the volume transport rates of sand along the
beach compute the incremental change in position of
each beach point :over a time interval, At. A Fortran
ENTRY statement links DERIV with that part of sub-
routine ADJUST that re-computes the incident angles
on some regular basis because of the re-shaping of
the shoreline.

6. Subroutine AREA

a. The surface area 'df the beach is an important

quantity. Its change can be monitored by co.p:uting
the area difference between two successive strand-
lines.. In Figure 4a the calculation is straightfor-
ward since the y coordinate of each endpoint remains
constant. Figure 4b represents the more general
case wherein the endpoints are allowed to move
freely. A rough estimate of the net areal change
(additions due to accretion minus depletions due
to erosion) can be had in the following way: (i)
connect the endpoints A, B and E, F as shown, (ii)
compute area under curves AF and BE (summations
over a series of trapezoids); these are the exact
areas under a discrete beach which is itself an
approximation to the real strandline, (iii) compute
the areas of trapezoids ABCD and EFGH, (iv) sub-
tract the two numbers in (ii) and, then, from this
result subtract the areas computed in (iii); this
number represents crudely the increase or decrease
in beach area. If the positive or negative con-
tribution near an endpoint is desired we can esti-
mate this at the left end to be ABA' where A' is
the point on curve AF at.which a line dropped from
B parallel to the vertical axis intersects. The
x coordinate of point A' is determined by linearly
interpolating between the beach points on either
side. The area, then, is just the area under AA'
minus the area ABCD. Similarly, the area EFE' can
be computed.
b. Approximate volumetric changes can be obtained by
multiplying the discrete trapezoidal areas by the
local value of Db.(see Figure 2).